Kinda late, but I thought that there are typically corrective measures that try to prevent oncogenes from kicking off. The key difference between "accumulated lightning bolts" and the final model chosen is that "accumulated lightning bolts" assumes a more or less fixed rates of lightning bolts, while the final model essentially that the rate of lightning bolts will increase over time, which corresponds well to an interpretation of long-term decay of corrective measures - such as replication error detection systems.
I think the key point is that systems for retaining homeostasis (so second order systems I guess) are themselves subject to degradation.
There are some cancers driven by things like mismatch-repair defects, so that the amount of DNA damage grows very quickly over time, but these don't cause the majority of cancers. In liquid (blood) tumors, especially, these are very rare - The predominant mechanism is just the accumulation of random defects due to cellular division.
On the other end of the scale are things like automobile accidents, where incidence peaks in teenage years and decreases thereafter (with a possible second peak as vision and reflexes deteriorate in the elderly). My point is that neither of these fit the neat curve drawn by the author. When everything is lumped together, the curve fits, but trying to draw broad conclusions about mechanisms from that kind of aggregate data is foolish.
I think the key point is that systems for retaining homeostasis (so second order systems I guess) are themselves subject to degradation.